Its been awhile since I worked on that stuff but there are two sets on windings in the motor. A low speed set to get the motor running and a high speed set for running speed.
There is a centrifugal switch that once the motor reaches a certain RPM it switches over to the high speed windings. It could be that the switch is stuck. You will have to remove the motor, tear it down and clean it out, figure out the switch, clean and lube it.
Often the motors in table saws would get packed with saw dust and cause the switch is get stuck in one position or another.
Warning!!!! There is a capacitor attached to it that will give a nasty jolt! It will most likely in a "hump" attached to the outside of the case. Remove the cover from it then carefully without touching the terminals with your fingers lay a screwdriver across the terminals to discharge the capacitor. Once that is done you can safely unhook the terminals and remove the capacitor and work on the motor.
Also check that the motor is wired up correctly for 110V. You can compare to the other one. Some motors can be wired for 110V or 220V. If someone wired it for 220V and you hooked it only to 110V that would cause some problems. Usually the motor will have a decal or plate stating 110/220 if its a dual voltage motor.